Two students are given cubic boxes, measuring 10 cm on a side. Robert puts a single glass marble with a
diameter of 10 cm in the box. Susan puts 1,000 1-cm glass marbles in her box.

1. Whose box has more empty space? Explain.

Answers

Answer 1

Answer:

Both boxes have the same amount of empty space

Explanation:

Given

Cube Box

[tex]Length = 10cm[/tex]

Robert:

1 glass marble

[tex]Diameter = 10cm[/tex]

Susan:

1000 glass marble

[tex]Diameter = 1cm[/tex]

Required

Whose box has more empty space?

First, we need to calculate the volume of the cubic box.

[tex]Volume = Length^3[/tex]

Substitute 10cm for Length

[tex]Volume = 10^3[/tex]

[tex]Volume = 1000cm^3[/tex]

Next, calculate the volume of Robert's glass

Volume is calculated as:

[tex]Volume = \frac{4}{3}\pi r^3[/tex] ---- Volume of a sphere

Where

r = radius

[tex]r = \frac{1}{2} * Diameter[/tex]

[tex]Diameter = 10cm[/tex] --- Given

Substitute 10 for diameter

[tex]r = \frac{1}{2} * 10cm[/tex]

[tex]r = 5cm[/tex]

So:

[tex]Volume = \frac{4}{3}\pi r^3[/tex]

[tex]Volume = \frac{4}{3} * \frac{22}{7} * 5^3[/tex]

[tex]Volume = \frac{4}{3} * \frac{22}{7} * 125[/tex]

[tex]Volume = 523.8cm^3[/tex]

Next, we determine the volume of Susan's 1000 glasses

Volume is calculated as:

[tex]Volume = \frac{4}{3}\pi r^3[/tex] ---- Volume of a sphere

Where

r = radius

[tex]r = \frac{1}{2} * Diameter[/tex]

[tex]Diameter = 1cm[/tex] --- Given

Substitute 1cm for diameter

[tex]r = \frac{1}{2} * 1cm[/tex]

[tex]r = 0.5cm[/tex]

Substitute 0.5cm for radius in [tex]Volume = \frac{4}{3}\pi r^3[/tex]

[tex]Volume = \frac{4}{3} * \frac{22}{7} * 0.5^3[/tex]

[tex]Volume = \frac{4}{3} * \frac{22}{7} * 0.125[/tex]

[tex]Volume = 0.5238[/tex]

But there are 1000 glasses.

So, the volume of 1000 glasses is:

[tex]Volume = 0.5238 * 1000[/tex]

[tex]Volume = 523.8cm^3[/tex]

--------------------------------------------------------------------------------------------------------------

For Robert:

[tex]Volume = 523.8cm^3[/tex]

For Susan:

[tex]Volume = 523.8cm^3[/tex]

Since, they have the same volume.

Both boxes have the same amount of empty space

Answer 2

From the dimensions of glass marble for robert and susan, we can say that; none of the given boxes have more empty space.

We are told that the cubic boxes have a measure of 10 cm for its' sides.

Formula for volume of a cube is;

V = lwh

where;

l is length

w is width

h is height

Thus; V = 10 × 10 × 10

V = 1000 cm³

For Robert;

We are told that he puts a glass marble with a diameter of 10 cm in the box. The glass is usually spherical in shape and the volume of a sphere is;

V = ⁴/₃πr³

Thus;

V_rob = ⁴/₃π × (10/2)³

V_rob = 523.6 cm³

Volume left for rob = 1000 - 523.6

Volume of empty space left for rob = 476.4 cm³

For Susan;

V = ⁴/₃πr³

Thus;

V_sus = ⁴/₃π × (1/2)³ × 1000

V_sus = 523.6 cm³

Volume left for susan = 1000 - 523.6

Volume of empty space left for susan = 476.4 cm³

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Related Questions

BRAINLIEST ✨✨✨

You can use the half-life Gizmo to model the decay of Carbon-14, which has a half like of approximately 6,000 years.
Use the Gizmo to estimate the age of each of the objects below For these questions, each second in the Gizmo represents 1,000 years.

Answers

Answer:

yes i thank..

Explanation:

i hope this helps

The granite most likely was formed by the process of A) compaction and cementation B) erosion and deposition © heating and metamorphism D) melting and soliditation​

Answers

Answer:

D) melting and soliditation​

Explanation:

Granite is a type of grainy (medium-coarse) igneous rock. These are formed from quartz, alkali feldspar and trace minerals along with plagioclase. Rocks like quartz, form a crystal from magma or as a precipitate near hydrothermal vents.

A type of intrusive igneous rock, granite is formed from its constituents when it molten rock cooled. Larger mineral crystals are associated with slower cooling over time.

Explain how a concentration gradient, a membrane protein, and hydrogen ions work together to provide a mitochondrion with the energy needed to join small molecules together. (6 points)

pls help asap :)

Answers

Answer:

you combine all the molicules

Explanation:

A concentration gradient, a membrane protein, and hydrogen ions work together to provide a mitochondria with the energy needed to join small molecules together through ATP. The H+ ions are pumped across by membrane “pump proteins” into a space bounded by memb ranes that contain numerous amounts of hydrogen ions. Then, electrons are passed from o ne membrane-bound enzyme to another, which causes some energy to get lost during eac h transfer. This “lost energy” allows the pumping of hydrogen ions against the concentratio n gradient. After all the steps are taken, the mitochondrion will be provided with the energy needed to join small molecules together.

When going to a higher power, where should the object be placed in the field of view?

Answers

Answer:

Return to the previous (lower power) objective.

Center the object in the field of view.

Go to the higher power objective and use only the fine focus.

Explanation:

what are NADH and FADH ? why are they important

Answers

Answer:

NADH: High energy electron carrier used to transport electrons generated in Glycolysis and Krebs Cycle to the Electron Transport Chain. FADH2: High energy electron carrier used to transport electrons generated in Glycolysis and Krebs Cycle to the Electron Transport Chain.

Explanation:

Answer:  Here you go!

NADH: NADH is the abbreviation for the naturally occurring biological substance, nicotinamide adenine dinucleotide hydride. ... Often referred to as coenzyme 1, NADH is the body's top-ranked coenzyme, a facilitator of numerous biological reactions.

FADH: Flavin adenine dinucleotide, or FADH2, is a redox cofactor that is created during the Krebs cycle and utilized during the last part of respiration, the electron transport chain. Nicotinamide adenine dinucleotide, or NADH, is a similar compound used more actively in the electron transport chain as well.

WHY ARE THEY IMPORTANT??

ATP production is an important part of cellular respiration (the process of generating energy from food) and both NADH and FADH2 that are involved in this process help in making more ATP. ... NADH and FADH2 that act as electron carriers give away their electrons to the electron transport chain.

explain why adding protons to the treated mitochondria increase ATP synthesis?​

Answers

Answer:

Because protons are no longer being used to power the ATP synthase, the proton gradient is not dissipated; the increasingly steep proton gradient makes it increasingly difficult for the electron-transport proteins to pump protons out of the matrix, and electron transport quickly stops.

Explanation:

Hope this helped!

Mitochondria are the power-house of the cell, which are primarily involved in the synthesis of Adenosine Triphosphate (ATP). The synthesis of ATP is mediated by the proton pump and electron transport chain.

The protons generate the gradient, which is produced by the proton-pumping during the electron transport chain. The increase in the mitochondrial ATP production is mediated by the activated SIRT1 and AMPK.

The protons then flow down the concentration gradient into the matrix through ATP synthetase, a membrane protein.

The gradient will cause the spinning and catalyze the conversion of ADP into ATP.

Therefore, the metabolic machinery of the ATP synthesis in the mitochondria will be increased due to the proton pump.

To know more about mitochondria and ATP synthesis, refer to the following link:

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a) Explain why antibiotics would kill a prokaryotic cell. (2 points)

Answers

Answer:

Antibiotics are simply chemicals that kill prokaryotic cells but do not harm eukaryotic cells. They are natural chemicals produced by fungi and bacteria that act to control their bacterial competitors. For example, streptomycin stops protein synthesis in prokaryotic cells by binding to their unusual ribosomes.

Explanation:

Sorry if this makes no sense. Basically, the antibiotics will harm/kill cells like the prokaryotic cell, but it won't harm or kill any human cells that are essential. They'll kill bacteria, though. The chemicals in the antibiotics aren't compatible with the ones in the prokaryotic cell, so it'll kill it.

If the endoplasmic reticulum were removed from the cell,which organelle would not be able to function properly, and why

Answers

Answer:

Golgi apparatus

Explanation:

Because it packages proteins received from the endoplasmic reticulum.

Explain why two turns of the Krebs cycle are needed for each molecule of glucose ?

Answers

the molecule that began the Krebs cycle. This molecule is needed for the next turn through the cycle. Two turns are needed because glycolysis produces two pyruvic acid molecules when it splits glucose

Two turns of the Krebs cycle are needed for each molecule of glucose

because glycolysis produces 2 molecules of pyruvate.

Glycolysis involves conversion of glucose to pyruvate after which it enters into the kreb's cycle to be converted into ATP which is the energy currency of cells.

Pyruvate is the substrate-compound which enters into the kreb's cycle to form ATP. Since we are dealing with two pyruvates which are products of glycolysis then two turns are needed.

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*
1. The_regulates what goes in and out of the cell.
cytoplasm
ribosomes
cell membrane
nucleus

Answers

Answer:

cell membrane

Explanation:

it controls what comes in an out of the cell if its a plant cell you would have the ell wall as well

26. Evolutionary relationships can be used to answer what kinds of questions?​

Answers

Answer:

To build phylogenetic trees, scientists must collect character information that allows them to make evolutionary connections between organisms. Using morphologic and molecular data, scientists work to identify homologous characteristics and genes.

Explanation:

Answer: structural similarities. factors that help determine evolutionary relationships: these similarities show that species are closely related and may have evolved from a common ancestor.

Styles
Edit
The diagram shows a root hair cell.
cytoplasm
vacuole
10
mitochondria
nucleus
Why does a root hair cell contain a large number of mitochondria?
A to provide energy for the absorption of water from the soil
B to provide energy for the diffusion of mineral ions from the soil
С to provide energy for osmosis
D to provide energy for the active transport of mineral ions from the soil |

Answers

Answer:

ambot lang kapuya da mura tag tae ani

Answer:

to provide enery for the active transport of minerals ions from soil

1. Explain how forces of attraction and repulsion exist within an atom.

Answers

Answer:

Oppositely charged particles attract each other, while like particles repel one another. Electrons are kept in the orbit around the nucleus by the electromagnetic force, because the nucleus in the center of the atom is positively charged and attracts the negatively charged electrons.

Explanation:

Answer:

1. Electrons surrounding a nucleus are attracted to the protons within it because electrons and protons have opposite charges. Electrons closest to the nucleus are attracted with such a force that they can’t escape from the atom. These electrons tend to shield the protons from electrons that are farther away because electrons have the same charge and repel each other. Electrons that are farther away have less attraction to the protons within the nucleus and are more likely to be detached from the atom.

2. Electrons can be transferred from atoms of one body to atoms of another body through friction. This can occur when one body is rubbed against another or when a liquid flows across a solid. In either case, one body may be given a positive charge while the other body is given a negative charge of the same magnitude. Both charges are developed at the same time. Electrons can also be transferred from one body to another when a charged body comes into contact with an uncharged body. The electrons move in the direction that will equalize the charges; thus, the uncharged body will be given the same charge as the charged body.

3. Free electrons move from points of negative charge to points of positive charge. When these electrons move freely from one point to another with little resistance, the material they’re traveling through is said to be a conductor. Conductors have a large number of free electrons. Insulators, on the other hand, have very few free electrons and offer great resistance to the movement of these electrons. Electric charges produced on one end of a body composed of insulating materials will most likely not spread throughout the body. In a conductor, this charge would spread throughout the entire body. Metals are generally conductors; oils, rubber, air, porcelain, and plastics are good insulators.

4.

Lightning is produced by the rapid transfer of free electrons when one of the following conditions exist: One part of a cloud is positively charged and a neighboring part of the same cloud is negatively charged. A positively charged cloud comes near a negatively charged cloud. A cloud with either a positive charge or a negative charge comes near the earth.

Explanation:

Pennfoster answer

Please help!!! What is a component of amino acid not contained in starch

A. Amino acids contain hydrogen.

B. Amino acids contain oxygen.

C. Amino acids contain carbon.

D. Amino acids contain nitrogen.

Answers

Answer:

D.

Explanation:

Nitrogen is the major atom that is present in amino acids that are not present in carbohydrates.

Answer:

Starch is a polysaccharide which comes under carbohydrates. The incorrect option here is option  D which says the basic constituent of amino acid, that contains nitrogen as it is not found in starch.

Explanation:

What is the basic component of starch?

Starch is a carbohydrate. Carbohydrates are of different types like monosaccharides, disaccharides, oligosaccharides, and polysaccharides. A monosaccharide is the basic simplest form of carbohydrate and a polysaccharide is the complex one.

The basic formula of any carbohydrate contains, Carbon, hydrogen and Oxygen. The polysaccharide, as the name suggests, it has many glucose molecules linked together as a chain.

Hence, starch is a polysaccharide found in plants. It is stored in the form of a storage molecule in plants. It does not contain nitrogen as its structural component.

learn more about the starch here

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How can speciation of plants benefit humans?

Answers

Answer:

Plant speciation can benefit humans by becoming draught resistant, of medicinal value, increased fruit ad seed bearing properties or insect resistant, to name a few.

The speciation of plants can help or benefit us humans by creating plants or crops that suit our specific needs.

how does the structure of fructose compare to the structure of glucose

Answers

Answer:

Glucose is an aldose and fructose is a ketose sugar.

Explanation:

They are isomers and they are both ketose sugars that are important building blocks for other sugars.

Glucose is an aldose and fructose is a ketose sugar.

what are the difference between glucose and fructose ?

glucose is a monosaccharide present in all major carbohydrates like starch, table sugar etc. It is the primary and preferred energy source of the body. Starch contains glucose.

It is also called as blood sugar or grape sugar which is a six-membered ring, form pyranose ring structure, is an aldohexose.

fructose is a monosaccharide, present in vegetables and fruits where The glycemic index is lower in fructose when compared to glucose.

The binding of fructose to protein in cell is seven times faster than glucose.

fructose are called as fruit sugar or D- fructose. Its functional group is the ketone, metabolized mainly in the liver. It is not found in starch.

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Which sensory regions of the brain are closest together? Which are furthest apart?

Answers

Answer:

1.Sensory areas are the areas of the brain that receive and process sensory information. The cerebral cortex is connected to various subcortical structures such as the thalamus and the basal ganglia. Most sensory information is routed to the cerebral cortex via the thalamus. 2.The main sensory areas of the brain include the primary auditory cortex, primary somatosensory cortex, and primary visual cortex. In general, the two hemispheres receive information from the opposite side of the body.

Explanation:

Sensory areas are the areas of the brain that receive and process sensory information.

What are the cerebral cortex and how it is connected?

The cerebral cortex is connected to various subcortical structures such as the thalamus and the basal ganglia. Most sensory information is routed to the cerebral cortex via the thalamus.The outer layer of the cerebrum. *Psychology* it's the grey bit. It's what makes us human, because of it's connection to consciousness and stuff like that.

The main sensory areas of the brain include the primary auditory cortex, primary somatosensory cortex, and primary visual cortex. Most sensory information is routed to the cerebral cortex via the thalamus.Sensory areas are the areas of the brain that receive and process sensory information. In general, the two hemispheres receive information from the opposite side of the body.

Therefore, Sensory areas are the areas of the brain that receive and process sensory information.

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Suppose the DNA sequence GCT ATA TCG was changed to GCTАТТ TCG. How would the products of translation, the amino acids, be affected ?

Answers

Answer:

The outcome of a frameshift mutation is complete alteration of the amino acid sequence of a protein. This alteration occurs during translation because ribosomes read the mRNA strand in terms of codons, or groups of three nucleotides. ... Each word itself has a separate meaning, as each codons represents one amino acid.

Explanation:

hope it helps.

have a wonderful day!

In the given DNA sequence GCT ATA TCG, the second codon is changed from ATA to АТТ.

This change would affect the products of translation, which are the amino acids. To determine the amino acids, we need to refer to the genetic code, which translates each codon into a specific amino acid. The codon ATA corresponds to the amino acid isoleucine (I), while the codon АТТ also corresponds to isoleucine (I).

Since both codons, ATA and АТТ, code for the same amino acid (isoleucine), the change in the second codon would not affect the amino acids produced during translation. Therefore, the products of translation, the amino acids, would remain unaffected by this change.

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3. After nuclear explosions animals and
humans can continue to die due to
ingestion of radioactive particles and
nuclear
A.fallout
B.rainout
C.whiteout

Answers

Answer:

A

Explanation:

The term was coined from the idea that the radioactive material would mix with the debris thrown in the air from the explosion.

A.fallout pls give brainliest

which structure makes proteins using instructions from the nucleus

Answers

Answer:

ribosomes

Explanation:

Ribosomes are small particles of RNA and protein found throughout the cytoplasm. Proteins are assembled on ribosomes. The nucleus gives coded instructions to the ribosomes, so they know what proteins to build.

what are
principle basis on classification​

Answers

Answer:

Classification is a systematic ordering of the object of research, in this case, ecosystems at the earth's surface or, in other words: landscape units as 'holons'. As for general principles of classification, we can learn a lot from the best-known classification, the taxonomical classification of species.

Explanation:

NEED HELP!!!!!! QUICK PLEASE!

Answers

Answer:

Last one

Explanation:

I took this test

Answer:

its D, it can make earths climates warmer.

Which of the following shows a correct base pairing in DNA?
A and G
T and G
C and A
Gand C

Answers

I think it is G and C

Answer: G and C

Explanation:  DNA carries the hereditary information for organisms. W ithout DNA, our species would be unable to pass traits from generation to generation. DNA controls all aspects of an organism. It tells spiders how to spin webs, birds to lay eggs, and what color to make your eyes. The genetic information in DNA is stored as special chemical sequences, called chemical bases. The chemicals bases are adenine (A), guanine (G), cytosine (C), and thymine (T). Each base connects with another to form base pairs. Adenine always pairs up with thymine. Cytosine always pairs up with guanine

What is the definition of:
Autotroph
Heterotroph
Decomposer
Unicellular
multicellular

Answers

Answer:

Autotroph: an organism capable of making its own food from carbon dioxide.

Heterotroph: an organism that cannot make its own food and thus has to eat either autotrophs or other heterotrophs for energy.

Decomposer: an organism that breaks down dead or decaying organisms; such decomposers are bacteria and fungi.

Unicellular: an organism that consists of one cell, such as bacteria. Some unicellular organisms have a nucleus and are called eukaryotes, while some have no nucleus, such as bacteria, which are called prokaryotes.

Multicellular: an organism that consists of many cells, such as you and I, and many other animals.

Hope this helps :)

Which title best reflects the main idea of the passage?

The Sun transfers energy in the form of heat to Earth through radiation. The ground gets warmer as heat flows from one ground particle (such as soil particles or rocks) to another. The ground heats up the air above it through conduction when the particles of air absorb heat from the particles of the ground. Heat also flows from the ground to the air through radiation. The warmed mass of air becomes less dense and rises. As it rises, it loses heat to the environment, so it cools and becomes more dense. The cool, dense air sinks and takes the place of the warm, less dense air. This convection process transfers heat from Earth’s surface to the atmosphere and moves heat around Earth.

Answers

Answer:

B: The Role of Heat Transfer Methods in the Distribution of Earth's Energy

Explanation:

Just took the question

Answer:

b

Explanation:

In what stage of sleep do you experience a high level of motor cortex activity (the part of the brain involved in the planning, control, and execution of voluntary movements) that is blocked by the brainstem, leaving you more-or-less temporarily paralyzed?

Answers

Answer: REM

Explanation:

There are four stages, 3 of them are non-REM stages, (or NREM) and obviously, the other is the REM stage.

We are looking for a stage where your body becomes "paralyzed".

This would be the REM sleep stage.

This is the stage where most of your dreams happen, and that is why your body is more-or-less paralyzed, so you do not move while dreaming.

There are other characteristics, like irregular (and faster) breathing and an increase in blood pressure and heart rate.

which series lists the structural components of the light-dependents reactions in order, from smallest to largest​

Answers

Answer:

Chlorophyll >thylakoid> grana >chloroplast.

Explanation:

Which type of cell is found in plants and animals? *
Amniotic
Eukaryotic
Ketonic
Prokaryotic

Answers

Answer:

Eukaryotic

Explanation:

This is the answer because:

Both plant and animal cells are eukaryotic cells, therefore, they contain membrane-bound organelles. For example, the nucleus, mitochondria, reticulum, golgi apparatus, and lysosomes.

Hope this helps!

Answer:

Eukaryotic

Explanation:

just did on flvs\

What are the different nutrients used for the body's cells?

Answers

Answer:

There are six classes of essential nutrients required for the body to function and maintain overall health. These six classes of essential nutrients are: carbohydrates, lipids (fats), proteins, water, vitamins, and minerals.

Explanation:

Consider the survey form in figure 8.2. Based on the information on the survey form,
what hypothesis can you possibly make? Relate demographics to the questions in the
survey form.

Answers

Oky I would love to help you but where is the image
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